![avinashpolwah](/avatars/31572.jpg)
avinashpolwah
14.02.2020 •
Mathematics
Consider the initial value problem
4u'' − u' + 2u = 0, u(0) = 3, u'(0) = 0.
(a) Find the solution u(t) of this problem.
(b) For t > 0, find the first time at which |u(t)| = 10. Round your answer to four decimal places.
Solved
Show answers
More tips
- S Science and Technology Discovering the Anatomy of an LCD TV Screen...
- F Family and Home How to Raise a Genius? Discover the Secrets Here...
- F Food and Cooking How to Properly Cook Buckwheat?...
- H Health and Medicine How to Tan in a Tanning Bed? Tips and Recommendations...
- S Style and Beauty How to Sew a Balloon Skirt: Detailed Tutorial and Tips on Choosing the Right Fabric...
- P Philosophy Personal attitude towards Confession: how to prepare and undergo the procedure correctly?...
- F Food and Cooking How to Make Cottage Cheese at Home: Simple and Quick Recipe with Step By Step Instructions...
- H Health and Medicine Which Water Are You Drinking? Is it Worth Buying Bottled Water?...
- H Health and Medicine What Makes a Man a Man?...
- H Health and Medicine What to Take with You to the Maternity Hospital?...
Answers on questions: Mathematics
- M Mathematics Choose the correct correspondence...
- C Chemistry Consult conceptual example 5 for background pertinent to this problem. a lead sphere has a diameter that is 0.050% larger than the inner diameter of a steel ring when...
- S Social Studies Which new concept did the sung dynasty introduce to japan and korea a. the religion of bhuddismb. the idea ot geishac. the principle of taxesd. the use of paper money...
- H History Did the jury really consider Tom Robinson to be innocent until proven guilty? Why or why not? Cite evidence as support....
Ответ:
Answer with Step-by-step explanation:
We are given that initial value problem
a.![4u''-u'+2u=0](/tpl/images/0511/0562/0acf0.png)
u(0)=3,u'(0)=0
Auxillary equation
By using quadratic formula:![x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}](/tpl/images/0511/0562/77630.png)
Therefore, the general solution of the initial value problem
Substitute t=0 and u(0)=3
Differentiate w.r.t t
Substitute t=0 and u'(0)=0
Substitute the value of![c_1](/tpl/images/0511/0562/6eee1.png)
Substitute the values
(b) For t>0![\mid u(t)\mid=10](/tpl/images/0511/0562/9b2a3.png)
We cannot find the solution of
analytically
But we can use the graph to find the approximate value of the solution.
By graph , the approximate value of t=12.2 for which![\mid u(t)\mid=10](/tpl/images/0511/0562/9b2a3.png)
Ответ:
what you want to say by this question